Arsenal just won't lie down. An eighth successive season without a trophy may stick in the craw but the lure of qualifying for the Champions League, for what would be a 16th consecutive campaign, remains as inviting as ever. Not to mention finishing above Tottenham Hotspur, their north London rivals. Nor, for that matter, Chelsea.

That Arsenal won at a canter against Reading at the Emirates Stadium yesterday says everything about their hunger to stay among the elite top four. Victory enabled them to maintain their four-point deficit to Tottenham, with a game in hand, but they closed the gap to fourth-placed Chelsea from five points to two.

If that hunger is still raging, which it appears to be, Arsenal were also helped in no small measure by a feeble display from Reading. Nigel Adkins, on his first match in charge since signing a three-year contract on Tuesday, might regret forsaking the easy life on sabbatical since he was dismissed by Southampton in January. Reading, it would seem, are doomed.

For Arsène Wenger, his Champions League season ticket could yet be renewed. "We enjoyed the game," the Arsenal manager, said. "And I enjoyed our technical and creative side and our spirit. It is a good basis for us to finish the season. We have to keep this attitude going.

"We are not in calculation mode. But it is now less predictable than it was predictable. We look at the table and we are still behind Tottenham and Chelsea. We will just try to win our next game and see where we stand. Let's give our all, we are a group that wants to go for it together."

Arsenal were depleted, with Theo Walcott, Jack Wilshere and Abou Diaby all absent injured. Still, they had scored 12 goals in their previous two meetings with Reading this season – the stunning 7-5 Capital One Cup fourth-round win, in which they recovered from 4-0 down after 37 minutes, and the 5-2 league victory. Both matches were at the Madejski Stadium.

Surely, there would be no mistake at the Emirates, against a Reading side who had lost five on the spin? Initially, it was tough going, but the 11th minute brought the breakthrough. Gervinho originated the move on the right and Olivier Giroud passed freely to Santi Cazorla on the left. The Spaniard clearly tried an angled effort on goal, which was careering well off-target, but Gervinho timed his dart to perfection to guide it past the former Arsenal goalkeeper Stuart Taylor from close range.

Let the fun begin. And it almost did, with Arsenal slicing Reading apart at will. All that they lacked was the finishing touch; if they had found it, the Berkshire team would have been dead and buried by half-time. But the home side, especially Gervinho, somehow contrived to squander chance after chance.

Arsenal should also have been awarded a penalty when Giroud ran through only to be "cleaned out" by the onrushing Taylor. Chris Foy, the referee, disagreed and, as the ball from Giroud's final touch bounced towards the empty net, Alex Pearce made the last-ditch clearance. Cazorla scuffed wide and Gervinho also drove over, completing a one-sided first half.

Three minutes into the second period, Arsenal were able to put one hand on cruise control. At the same time, another nail was hammered into Reading's relegation coffin as they plunged to the foot of the table, on goal difference from the non-playing Queens Park Rangers, who visit Fulham tomorrow.

Again, the frailties of the worst defence in the division – and the worst team away from home – were exposed for all to see. Arsenal's build-up was neat, with Cazorla exchanging passes with Gervinho, but the way in which they were allowed the freedom to do it was poor. However, Cazorla's execution was pure class, a delightful curling effort inside Taylor's left-hand upright.

Reading responded briefly when Pavel Pogrebnyak was denied by a fine tackle from Laurent Koscielny and Pearce volleyed at Lukasz Fabianski. However, they imploded once more when, from their own corner, Gervinho raced away down field and set up Giroud – the only team-mate to have bothered to follow him – to make it 3-0.

Yet suddenly, at 3-1, would Arsenal wobble? Hal Robson-Kanu had just stooped low to nod in a Jobi McAnuff cross to the far post. But it was just a blip as Adrian Mariappa rashly fouled the substitute Alex Oxlade-Chamberlain in the Reading area, perhaps marginally, and Mikel Arteta tucked in the penalty to makle.

"I still want to be managing in the Premier League," Adkins said. "It was always going to be a challenge, especially with the fragmented week we've had because of the internationals. We just have to concentrate on the now. We'll analyse this on Monday and take lessons from it."